I just removed mine on my 66....I took a tool and very easily lifted it off ..Mine were held on by a rubber grommit..The trim snaps in place over the grommit..The grommit fit's into the elongated hold in the doors and fenders.I pulled that out using the same tool...like a plastic puddy knife..go about it easy and I don't think you'll have any prob's....It's going to be different from my 66 I'm sure....
There are these little plastic clips spaced every 2'-2.5' holding it on from behind it. You will have to use bondo or weld the holes up after removing them and repaint. But you should be able to tweek the strip by rotating the top away from the body and it should pop off, start from the back and work forward. I'm not sure how the clips are attached but it shouldn't be too hard to figure out.
I removed the trim from my '74 two days ago...not sure if it is the same on the '71 but here is what I did.
There are three pieces of trim on each side, the back one has one bolt that you remove from inside the trunk. After you get that off the trim will pop off the 8 or so tabs that are on the Nova...pull the trim off carefully and it is really easy. Then remove the plastic tabs that are attached to metal tabs. I used a Dremel cutting wheel to grind the metal tabs off and down.
The middle piece of trim is just like the back one except there are 2 bolts, both at either ends of the door. Remove those, pop off trim, pop off plastic piece, grind down metal tabs.
The front piece of trim is messier. There are no tabs, all of the connections are bolted in...I think there are 5 or 6. You can reach 2 or 3 of them from inside the bay. You can either take off the fenders and unbolt the trim that way or you can do what I did and take a big pair of pliers and rip the trim off. Obviously this ruins that section of trim but if that's fine with you then this is very easy to do. After that, grind or try and unscrew the bolts leaving behind the 5 05 6 holes...weld those up along with the 3 from the back two pieces.